Preheat the oven to 350°F (175°C). Grease the 9x13 inch baking pan and set aside.
In a medium saucepan over low heat, melt the butter. Remove from the heat and stir in the granulated sugar until fully combined.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract and the peppermint extract.
In another bowl, sift together the flour, cocoa powder, salt, and baking powder. Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Pour the brownie batter into the prepared baking pan and spread evenly. Bake for 25 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.
While the brownies cool, prepare the frosting. In a mixing bowl, beat the softened butter until smooth and creamy.
Gradually add the powdered sugar, alternating with the milk, until you reach a smooth consistency. Mix in the peppermint extract.
Once the brownies are completely cool, spread the peppermint frosting evenly on top.
Sprinkle the crushed candy canes over the frosted brownies.
Cut into 12 equal pieces and serve.